The purpose of this paper is to provide a short summary of some recent developments in the geometry of discrete structures. Clearly choosing topics of such an exposition the author's personal taste has played an important role. The emphasis lies on oriented matroid theory. The survey starts with a brief introduction into the theory of computational complexity explaining the meaning of 'easy'', ''hard'' and 'intractable'' problems. While emphasizing the role of a duality theory for developing efficient algorithms the rest of the paper considers oriented matroids from a linear programming point of view
